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7.2: Parametric Equations
https://math.libretexts.org/Workbench/MAT_2420_Calculus_II/07%3A_Parametric_Equations_and_Polar_Coordinates/7.02%3A_Parametric_Equations
In this section we examine parametric equations and their graphs. In the two-dimensional coordinate system, parametric equations are useful for describing curves that are not necessarily functions. Th...In this section we examine parametric equations and their graphs. In the two-dimensional coordinate system, parametric equations are useful for describing curves that are not necessarily functions. The parameter is an independent variable that both x and y depend on, and as the parameter increases, the values of x and y trace out a path along a plane curve.
10.8: Parametric Equations- Graphs
https://math.libretexts.org/Workbench/Algebra_and_Trigonometry_2e_(OpenStax)/10%3A_Further_Applications_of_Trigonometry/10.08%3A_Parametric_Equations-_Graphs
In this section, we’ll discuss parametric equations and some common applications, such as projectile motion problems.
6.1: Parametric Equations
https://math.libretexts.org/Courses/SUNY_Geneseo/Math_222_Calculus_2/06%3A_Parametric_Equations_and_Polar_Coordinates/6.01%3A_Parametric_Equations
In this section we examine parametric equations and their graphs. In the two-dimensional coordinate system, parametric equations are useful for describing curves that are not necessarily functions. Th...In this section we examine parametric equations and their graphs. In the two-dimensional coordinate system, parametric equations are useful for describing curves that are not necessarily functions. The parameter is an independent variable that both x and y depend on, and as the parameter increases, the values of x and y trace out a path along a plane curve.
Section 17.14: Geogebra visual- parametric equations of an ellipse in a horizontal plane
https://math.libretexts.org/Courses/Al_Akhawayn_University/MTH2301_Multivariable_Calculus/17%3A_Visualizations/17.14%3A_Geogebra_visual-_parametric_equations_of_an_ellipse_in_a_horizontal_plane
4.3: Lines and Planes
https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/04%3A_R/4.03%3A_Lines_and_Planes
We can use the concept of vectors and points to find equations for arbitrary lines in $\mathbb{R}^n$ , although in this section the focus will be on lines in $\mathbb{R}^3$ .
5.1: Parametric Equations
https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/05%3A_Differential_Calculus_with_Parametric_Curves/5.01%3A_Parametric_Equations
In this section we examine parametric equations and their graphs. In the two-dimensional coordinate system, parametric equations are useful for describing curves that are not necessarily functions. Th...In this section we examine parametric equations and their graphs. In the two-dimensional coordinate system, parametric equations are useful for describing curves that are not necessarily functions. The parameter is an independent variable that both x and y depend on, and as the parameter increases, the values of x and y trace out a path along a plane curve.
10.6: Parametric Equations
https://math.libretexts.org/Bookshelves/Algebra/Algebra_and_Trigonometry_1e_(OpenStax)/10%3A_Further_Applications_of_Trigonometry/10.06%3A_Parametric_Equations
We begin this section with a look at the basic components of parametric equations and what it means to parameterize a curve. Then we will learn how to eliminate the parameter, translate the equations ...We begin this section with a look at the basic components of parametric equations and what it means to parameterize a curve. Then we will learn how to eliminate the parameter, translate the equations of a curve defined parametrically into rectangular equations, and find the parametric equations for curves defined by rectangular equations.
10.2: Parametric Equations
https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus/10%3A_Parametric_Equations_and_Polar_Coordinates/10.02%3A_Parametric_Equations
This section introduces parametric equations, where two separate equations define $x$ and $y$ as functions of a third variable, usually $t$ . It explains how to graph parametric curves, eliminate...This section introduces parametric equations, where two separate equations define $x$ and $y$ as functions of a third variable, usually $t$ . It explains how to graph parametric curves, eliminate the parameter to find Cartesian equations, and analyze motion along a path. Examples illustrate the flexibility of parametric equations in describing curves that are difficult to express in standard Cartesian form.
9.6: Vector-Valued Functions
https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Active_Calculus_(Boelkins_et_al.)/09%3A_Multivariable_and_Vector_Functions/9.06%3A_Vector-Valued_Functions
In $\mathbb{R}^2\text{,}$ a parameterization of a curve is a pair of equations $x = x(t)$ and $y = y(t)$ that describes the coordinates of a point $(x,y)$ on the curve in terms of a parameter ...In $\mathbb{R}^2\text{,}$ a parameterization of a curve is a pair of equations $x = x(t)$ and $y = y(t)$ that describes the coordinates of a point $(x,y)$ on the curve in terms of a parameter $t\text{.}$ In $\mathbb{R}^3\text{,}$ a parameterization of a curve is a set of three equations $x = x(t)\text{,}$ $y=y(t)\text{,}$ and $z = z(t)$ that describes the coordinates of a point $(x,y,z)$ on the curve in terms of a parameter $t\text{.}$
10.7: Parametric Equations
https://math.libretexts.org/Workbench/Algebra_and_Trigonometry_2e_(OpenStax)/10%3A_Further_Applications_of_Trigonometry/10.07%3A_Parametric_Equations
We begin this section with a look at the basic components of parametric equations and what it means to parameterize a curve. Then we will learn how to eliminate the parameter, translate the equations ...We begin this section with a look at the basic components of parametric equations and what it means to parameterize a curve. Then we will learn how to eliminate the parameter, translate the equations of a curve defined parametrically into rectangular equations, and find the parametric equations for curves defined by rectangular equations.
5.1: Parametric Equations
https://math.libretexts.org/Courses/Cosumnes_River_College/Math_401%3A_Calculus_II_-_Integral_Calculus/05%3A_Parametric_Equations_and_Polar_Coordinates/5.01%3A_Parametric_Equations
This section introduces parametric equations, where two separate equations define $x$ and $y$ as functions of a third variable, usually $t$ . It explains how to graph parametric curves, eliminate...This section introduces parametric equations, where two separate equations define $x$ and $y$ as functions of a third variable, usually $t$ . It explains how to graph parametric curves, eliminate the parameter to find Cartesian equations, and analyze motion along a path. Examples illustrate the flexibility of parametric equations in describing curves that are difficult to express in standard Cartesian form.

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